If $y=\cos ^{-1}(\cos x)$, then find $\frac{d y}{d x}$ at $x=\frac{5 \pi}{4}$

Question

Aicharya · Accepted Answer

$\begin{aligned} & y=\cos ^{-1}(\cos x) \ & y=\cos ^{-1}(\cos (2 \pi-x)) \quad[\because x \in(\pi, 2 \pi)]\end{aligned}$ $\begin{aligned} y & =2 \pi-x \ \frac{d y}{d x} & =-1\end{aligned}$

If $y=\cos ^{-1}(\cos x)$, then find $\frac{d y}{d x}$ at $x=\frac{5 \pi}{4}$

Solution